What is the mathematical relationship between the length of two line segments, each of which extends radially (perpendicularly) from a separate point on a circle to a line which is tangent to a third point on the circle?
For example, the following diagram shows a circle with origin o and radius r (not = 1) which is centered on the intersection of horizontal axis x and vertical axis y. Line z is tangent to the circle at point p which is the top intersection of the circle and vertical axis y. Line segments s & t (red & green respectively) each begin on the circle and extend radially to line x. Angle a is formed by the vertical axis y and the radial extension of line segment s while angle b is formed by the radial extensions of line segments s & t. Arc d extends from the origin of line segment s to the origin of line segment t.
1) What is the mathematical relationship between the length of line segments s & t?
2) What is the length of arc d (may be expressed in radians)?